Uploaded by cfurse on 24.08.2009

Transcript:

Welcome to ECE3300 at the University of Utah. This is

an introduction to electromagnetics and we are going to

begin with with lecture number one, which is a review

of the electric and magnetic fields, the forces

associated with them and their sources. The electric

field is described by coulomb's law. You've seen

coulomb's law before in physics. What it says is if

you have two like charges, either both positive or both

negative, that they are going to repell. And if you

have two charges of different polarity, a positive and

a negative charge, they are going to tend to attract.

let's call this this charge q1 and lets call this

charge q2. The magnitude of the force associated with

either of these two charges is found by multiplying the

charges q1 x q2 dividing by 4 pie epsilon naught and

then the distant squared between them. This right here

is r12, that's the distance from charge number one to

charge number two. The forces given in newton's, the

charges are given in coulomb's and of course the

distance is given in meters. We all know that the

force is a vector quantity, this force right here is

the force on charge two, caused by charge one and it is

going to be the opposite of the force on charge one,

caused by charge two. So force 1 2 is going to be the

negative of force 2 1. Let's find force 2 1, force 2 1

is going to be the magnitude we have above, q1 divided

by -- sorry q1 x q2 divided by 4pi epsilon naught and

then the distance between them squared. And then we

need to define the direction. The direction right here

is going to be given by a unit vector r from 1 to 2,

and that's unit vector. So r from 1 to 2. Let me draw

that. R is going from one to two. That's the unit

vector that's describing the force on charge two caused

by charge number one. Over here, this would be the

unit vector from 2 to 1. There is a constant that is

important here. It is epsilon naught. It is called

the permittivity or the electrical permittivity. We

can see this is the permittivity of free space because

of the naught or the 0 that is shown here. The

magnitude of permittivity of free space

is 8.854 x 10 to the minus 12 farads per meter.

so this gives you us a complete picture of the force

that is caused by a charge. The electric field is associated

with this force. Let's take a charge right here and a

charge right there, q1, q2 and let's say that we want

to find the electric field right here where q1 is. The

way we do that is we let q1 be one coulomb, sometimes

we call this taking a test chairing of one coulomb, and

putting it at the location we want to find the electric

field. The electric field will be a vector quantity

and it will be q1 x q2 over 4pi epsilon naught, r from

1 to 2 squared and it is going to be in which

direction? Right here. If we want to find the

electric field here we want the force on q1 so e at

location number one is going to be this. It is going

to be r from two to one, and that's going to tell us

the force that happens, that's caused by charge two at

the charge one location. This is the electric field at

that location number one.

an introduction to electromagnetics and we are going to

begin with with lecture number one, which is a review

of the electric and magnetic fields, the forces

associated with them and their sources. The electric

field is described by coulomb's law. You've seen

coulomb's law before in physics. What it says is if

you have two like charges, either both positive or both

negative, that they are going to repell. And if you

have two charges of different polarity, a positive and

a negative charge, they are going to tend to attract.

let's call this this charge q1 and lets call this

charge q2. The magnitude of the force associated with

either of these two charges is found by multiplying the

charges q1 x q2 dividing by 4 pie epsilon naught and

then the distant squared between them. This right here

is r12, that's the distance from charge number one to

charge number two. The forces given in newton's, the

charges are given in coulomb's and of course the

distance is given in meters. We all know that the

force is a vector quantity, this force right here is

the force on charge two, caused by charge one and it is

going to be the opposite of the force on charge one,

caused by charge two. So force 1 2 is going to be the

negative of force 2 1. Let's find force 2 1, force 2 1

is going to be the magnitude we have above, q1 divided

by -- sorry q1 x q2 divided by 4pi epsilon naught and

then the distance between them squared. And then we

need to define the direction. The direction right here

is going to be given by a unit vector r from 1 to 2,

and that's unit vector. So r from 1 to 2. Let me draw

that. R is going from one to two. That's the unit

vector that's describing the force on charge two caused

by charge number one. Over here, this would be the

unit vector from 2 to 1. There is a constant that is

important here. It is epsilon naught. It is called

the permittivity or the electrical permittivity. We

can see this is the permittivity of free space because

of the naught or the 0 that is shown here. The

magnitude of permittivity of free space

is 8.854 x 10 to the minus 12 farads per meter.

so this gives you us a complete picture of the force

that is caused by a charge. The electric field is associated

with this force. Let's take a charge right here and a

charge right there, q1, q2 and let's say that we want

to find the electric field right here where q1 is. The

way we do that is we let q1 be one coulomb, sometimes

we call this taking a test chairing of one coulomb, and

putting it at the location we want to find the electric

field. The electric field will be a vector quantity

and it will be q1 x q2 over 4pi epsilon naught, r from

1 to 2 squared and it is going to be in which

direction? Right here. If we want to find the

electric field here we want the force on q1 so e at

location number one is going to be this. It is going

to be r from two to one, and that's going to tell us

the force that happens, that's caused by charge two at

the charge one location. This is the electric field at

that location number one.